IQR in a list with an odd number of observations:
\(2, 3, 3, 4, 4, 6, 7, 7, 7, 8, 9, 11, 12\)
- Q1 is the median of the numbers below the median: \({\color{mathOrange} 2, 3, 3, 4, 4, 6,} {\color{mathBlue} 7},
7, 7, 8, 9, 11, 12\) (\(\frac{3 + 4}{2}\)) \(= {\color{mathOrange} 3.5}\)
- Q3 is the median of the numbers above the median: \(2, 3, 3, 4, 4, 6, {\color{mathBlue} 7},
{\color{mathRed}7, 7, 8, 9, 11, 12}\) (\(\frac{8 + 9}{2}\)) \(= {\color{mathRed} 8.5}\)
- Subtract Q1 from Q3: \({\color{mathRed} 8.5} - {\color{mathOrange} 3.5} = 5\)
IQR in a list with an even number of observations:
\(3, 4, 5, 7, 9, 10, 11, 13\)
- Q1 is the median of the numbers below the median: \({\color{mathOrange} 3, 4, 5, 7, }
9, 10, 11, 13\) (\(\frac{4 + 5}{2}\)) \(= {\color{mathOrange} 4.5}\)
- Q3 is the median of the numbers above the median: \(3, 4, 5, 7,
{\color{mathRed}9, 10, 11, 13}\) (\(\frac{10 + 11}{2}\)) \(= {\color{mathRed} 10.5}\)
- Subtract Q1 from Q3: \({\color{mathRed} 10.5} - {\color{mathOrange} 4.5} = 6\)
TIP: The median of the list is \(8\).